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A Contribution to Theory of Traffic Flow 680171

This paper presents an analysis of a car following model of general form: ẍn + 1 = A (ẋn -ẋn + 1)/(xn - xn + 1)m, where A and m are constants, xn + 1 is the position of the following car, xn the position of the followed car, ẋn + 1 and ẋn the corresponding velocities, and ẍn + 1 the acceleration of the following car. Several specific values of m are considered and their correlation with various traffic flow diagrams is established. Traffic flow in which all drivers, in line of vehicles, maintain a certain minimum safe distance is represented by the case, m = 0. The case, m = l, is shown to lead to a velocity-concentration curve due to Greenberg. The case, m = 2, is correlated with the rate of change of the visual perceptual angle of the follower and is shown to lead to Greenshields' velocity-concentration curve. Finally, the implications of the case when → ∞ are explored.